Mechanical Engineering

Horsepower Calculator

Convert between horsepower, watts, torque and RPM for engines, motors, and mechanical systems.

Formula HP = (T × RPM) / 9549.3Reviewed Sep 8, 2026

Horsepower (HP) is the standard unit of mechanical power used to rate engines, motors, pumps, and other rotating machinery. This calculator works in four modes: convert watts or kilowatts directly to horsepower, calculate horsepower from torque and RPM (the dynamometer method used for engines), or rearrange the formula to find the torque or RPM needed to produce a given horsepower. All calculations use SI base units internally and support both metric and imperial inputs.

Calculation Bench

Calculate

01Power

P · Electrical or mechanical power

Solution

Enter values above to calculate.

HP = P(W) / 745.7

Formula Sheet

HP = \dfrac{P_{\text{W}}}{745.7}

HP = \dfrac{T_{\text{N·m}} \times n}{9549.3}

T = \dfrac{HP \times 9549.3}{n}

n = \dfrac{HP \times 9549.3}{T_{\text{N·m}}}

HPHorsepower
PPower
TTorque
nRotational Speed
9549.3Conversion constant

Variables & Units

Symbol	Variable	Description	Common Units
HP	Horsepower	Mechanical power output. 1 HP = 745.7 W.
P	Power	Power in watts or kilowatts.	W, kW, MW
T	Torque	Rotational force applied at a radius from the axis of rotation.	N·m, lb·ft
n	Rotational Speed	Number of full revolutions per minute.	rpm
9549.3	Conversion constant	60,000 / (2π) - converts N·m × RPM to watts.

How to Use This Calculator

01Choose what you want to calculate: HP from Power (W/kW), HP from Torque + RPM, Torque from HP + RPM, or RPM from HP + Torque.
02For HP from Power: enter the power in watts or kilowatts.
03For HP from Torque + RPM: enter the torque (N·m or lb·ft) and the rotational speed (RPM).
04For Torque or RPM: enter the horsepower value and the known mechanical quantity.
05The calculator instantly shows the result with a secondary power-in-watts conversion.
06For electric motors, remember this is mechanical output power. If you are starting from electrical input current and voltage, check efficiency and power factor separately before comparing to shaft horsepower.

How the Formula Works

One mechanical horsepower is defined as exactly 550 foot-pounds per second, which equals 745.7 watts. This is the conversion factor used in all three power-based calculations.

For rotating machinery, power is the product of torque and angular velocity: P = T × ω, where ω (in radians per second) equals 2π × RPM / 60. Combining this with the HP conversion gives the standard formula HP = (T × RPM) / 9549.3 (for SI units), or HP = (T [lb·ft] × RPM) / 5252 for imperial.

The constant 5252 appears in the imperial formula because 33,000 ft·lbf/min ÷ (2π) ≈ 5252. The constant 9549.3 is the SI equivalent: 60,000 ÷ (2π).

All four solve modes are algebraic rearrangements of the same underlying equation P = T × 2π × n / 60, so results are always fully invertible.

Worked Example 01

Electric motor: 15 kW to HP

Known

Power (P): 15 kW = 15,000 W

Formula

HP = P(W) / 745.7

Substitution

HP = 15,000 / 745.7

Result

HP = 20.12 HP

A 15 kW electric motor produces approximately 20.1 mechanical horsepower. This is a very common conversion when reading European motor nameplates (which show kW) and comparing to North American equipment rated in HP.

Worked Example 02

Engine dyno: Torque + RPM to HP

Known

Torque (T): 400 N·m
Speed (n): 3500 RPM

Formula

HP = (T × RPM) / 9549.3

Substitution

HP = (400 × 3500) / 9549.3

Result

HP = 146.6 HP

An engine producing 400 N·m of torque at 3500 RPM generates about 146.6 horsepower at that speed. Peak horsepower occurs at a different RPM than peak torque - this is why engine dyno charts plot both curves against RPM.

Worked Example 03

Find required torque for a motor at target speed

Known

Horsepower (HP): 5 HP
Speed (n): 1750 RPM (typical 4-pole 60Hz motor)

Formula

T = (HP × 9549.3) / RPM

Substitution

T = (5 × 9549.3) / 1750

Result

T = 27.3 N·m

A 5 HP motor running at 1750 RPM (typical full-load speed of a standard US 4-pole, 60 Hz induction motor) must produce 27.3 N·m of torque at its shaft.

Applications

01Converting engine dyno data (torque + RPM curves) into a horsepower curve
02Sizing electric motors in kW for a required HP rating
03Calculating the torque a motor must produce at a given operating speed
04Checking if a gearbox or coupling is rated for the transmitted power
05Converting between kW and HP for equipment spec sheets and purchasing

Assumptions

01Uses mechanical/electrical horsepower (1 HP = 745.7 W). Metric horsepower (PS) = 735.5 W is not used here - check your engine spec sheet.
02Assumes steady-state, constant-speed operation. Does not account for transient loads, acceleration, or derating.
03Does not account for drivetrain losses - the result is shaft horsepower before transmission, gearbox, and final-drive friction.

Where This Model Stops

01Horsepower ratings vary by standard: SAE, DIN, and JIS each measure under different test conditions. Always match the formula to the rating system used.
02For accurate engine dyno results, you must also measure torque at the wheel (WHP) separately from shaft HP - this calculator computes shaft HP only.
03Does not account for power factor in electric motor HP calculations - for three-phase motors, see the Three-Phase Power Calculator.
04Does not include service factor, overload rating, starting torque, duty cycle, altitude derating, or gearbox/coupling efficiency.

References

[1]
SAE J1349 - Engine Power Test Code: Spark Ignition and Compression Ignition
SAE International
Defines the test conditions under which HP is measured for automotive engines.
[2]
ISO 80000-4 - Mechanics: Quantities and Units
International Organization for Standardization
Defines power units and the relationship between SI units for mechanical power.

Frequently Asked Questions

What is the difference between mechanical and metric horsepower?

Mechanical (US) horsepower = 745.7 W. Metric horsepower (PS, used in Europe) = 735.5 W - about 1.4% less. When converting European car specs to HP, this small difference matters. This calculator uses mechanical HP (745.7 W). Always confirm which standard your spec sheet uses.

Why does the imperial formula use 5252?

One horsepower is defined as 33,000 foot-pounds per minute. Rotational speed in RPM means each revolution covers 2π radians. Dividing 33,000 by 2π gives 5252.11 - rounded to 5252 in practice. So HP = T (lb·ft) × RPM / 5252.

Is this brake horsepower (BHP) or wheel horsepower (WHP)?

This calculator computes shaft power - equivalent to BHP when no drivetrain losses are present. WHP (at the wheels) is typically 10–15% lower after accounting for transmission, driveshaft, differential, and axle friction. To estimate WHP, multiply your BHP by a drivetrain efficiency factor (e.g. 0.85 for a manual gearbox).

My motor nameplate shows kW. How do I convert to HP?

Use the 'HP from Power' mode and enter the kW value - the calculator handles the conversion. As a quick reference: 1 kW ≈ 1.341 HP, so a 7.5 kW motor is approximately 10 HP.

How is this different from the Torque Calculator?

The Torque Calculator solves moment from force and radius. This Horsepower Calculator relates torque to rotational speed, so it is the right tool when you know RPM and want shaft power or required torque at speed.

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